I would like an "implementation" of a Wiki "TNB Frame"
helix with the center of the helix being a function in
three dimensions. The Wiki page shows an example of a
helix centered on a line. This project involves generalizing
that implementation to a helix center following a general
function g(x,y,z) in 3D. The formula for a line centered
helix are as follows,
g(x,y,z) is the center of the first order helix
z = a.z * t + b.z;
x = a.x * cos(2*pi*f.x*t + b.x);
y = a.y * sin(2*pi*f.y*t + b.y);
a.z,a.x,a.y are constants
b.z,b.x,b.y are constants
f.x and f.y are constants
This needs to be converted to from s(t) to s(x,y,z) as
described in the Wiki page. Then plotted and/or animated.
I estimate that this project is fairly easy for one well
versed in math.
A successful solution may result in more elaborate work.
I would like to have a Matlab solution, but a "pure"
mathematical might be more general and hence more
Development time is not critical, but generality is.
The next step will involve implementing a second helix
that is centered on the first helix which is centered
on a generalized 3-D curve.